Dynamics and structure of liquids under special conditions: water confined in giant polyoxometalates and co2-brine mixtures

L'estructura i la dinàmica dels líquids varien sota determinades condicions, tals com sota confinament o en presència d'ions. Aquesta tesi es divideix en dues parts. En la primera part, s'han estudiat l'estructura i la dinàmica d'aigua confinada en polyoxomolibdats gegants, per mitjà de simulacions de dinàmica molecular (DM) a condicions normals de temperatura i pressió. Els resultats obtinguts mostren que l'aigua tendeix a organitzar-se en capes concèntriques de la família de les buckyball. Les posicions d'aquestes capes coincideixen amb resultats experimentals de raigs X per aquest sistema a baixa temperatura. S'han calculat un gran nombre de propietats estructurals i dinàmiques, algunes de les quals s'han comparat amb dades experimentals i de simulació per micel•les reverses de grandària similar amb un resultat satisfactori. La segona part de la tesi es centra en el càlcul de la difussivitat del diòxid de carboni (CO2) en salmorra sota les condiciones termodinàmiques representatives d’aqüífers salins subterranis mitjançant simulacions de dinàmica molecular. S'han calculat els coeficients de difusió màssics i d'autodifusió del CO2, la conductivitat elèctrica de la barreja, així com els temps de relaxació rotacional del CO2 per totes les condicions. Aquests resultats constitueixen la primera estimació de coeficients de difusió màssics i temps de relaxació rotacional del CO2 en aqüífers salins subterranis.The structure and dynamics of liquids are distorted under special conditions, such as under confinement, or in the presence of ions. This thesis is divided into two parts. In the first part, we have studied the structure and dynamics of water confined in giant polyoxomolybdate molecular clusters by means of molecular dynamics (MD) simulations at ambient conditions. We observe that water organizes in concentric layered structures of the buckyball family, which agree with X-ray data for these systems at low temperature. Several structural and dynamical data are provided and compared to experimental and theoretical analyses for reverse micelles of similar size, where qualitative agreement is observed. The second part of the thesis is devoted to the calculation of the diffusivity of carbon dioxide (CO2) in brine under the thermodynamic conditions representative of deep saline aquifers through MD simulations. We have calculated CO2 mass and self diffusion coefficients, electrical conductivities, as well as rotational relaxation times. These results are the first estimation of mass diffusion and rotational relaxation times of CO2 in deep saline aquifers

Cut elimination for Zermelo set theory

We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys the normalization property. To do so, we first rephrase set theory as a theory of pointed graphs (following a paradigm due to P. Aczel) by interpreting set-theoretic equality as bisimilarity, and show that in this setting, Zermelo's axioms can be decomposed into graph-theoretic primitives that can be turned into rewrite rules. We then show that the theory we obtain in deduction modulo is a conservative extension of (a minor extension of) Zermelo set theory. Finally, we prove the normalization of the intuitionistic fragment of the theory

Completions of Implicative Assemblies

We continue our work on implicative assemblies by investigating under which circumstances a subset $M \subseteq \mathcal{S}$ of the separator gives rise to a full lex subcategory $\mathbf{Asm}_M$ of the quasitopos $\mathbf{Asm}_{\mathcal{A}}$ of all implicative assemblies such that ${\mathbf{Asm}_M}_{reg/lex} \simeq \mathbf{Asm}_{\mathcal{A}}$. We establish a characterisation. What is more, this characterisation is relevant to the study of $\mathbf{Asm}_M$'s ex-completion, which turns out to be a topos

Relative normalization

G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this property implies their consistency. When we cannot prove in a theory U the consistency of a theory T , we can try to prove a relative consistency theorem, that is, a theorem of the form: If U is consistent then T is consistent. Following the same spirit, we show in this paper how to prove relative normalization theorems, that is, theorems of the form: If U is 1-consistent, then T has the normalization property

A lambda-calculus with constructors

(avec annexes)International audienceWe present an extension of the lambda(eta)-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic `divide and conquer' technique by which we determine all the pairs of commuting subsystems of the formalism (considering all the possible combinations of the nine primitive reduction rules). Finally, we prove a separation theorem similar to Böhm's theorem for the whole formalism

El carst de sa Malafetge

[cat] Els autors, després d’una llarga prospecció espeleològica, presenten 15 formacions endocàrstiques situades a la serra de Son Camps (serra de na Burguesa), amb els seus respectius aixecaments topogràfics. Destaquen, pel seu recorregut, l’avenc des Cérvol (210 m), i, per l’abundant i variat concrecionament, la cova de sa Fantasia.[eng] After a long speleological exploration, the authors present 15 karstic caves situated on the Serra de Son Camps (Serra de Na Burguesa), with their respective surveys. Noteworthy are the Avenc des Cérvol, with a 210 meter survey length, and the Cova de sa Fantasia, for the abundance and variety of its speleothems.[ita] Gli autori, dopo una lunga prospezione speleologica, presentano 15 forme endocarsiche, con i suoi rispettivi innalzamenti topografici, che si situano nella Serra de Son Camps (Serra de na Burguesa). Risaltano, per il suo percorso, l’Avenc des Cervol (210 m), e per l’abbondanza e varietà del concrezionamento, la Cova de sa Fantasi

Les coves de cala Anguila

[cat] Presentam la topografia i la descripció de set cavitats del litoral de Manacor, que es troben a la urbanització de Portocristo Novo. Aquestes formacions endocàrstiques es localitzen a la plataforma tabular postorogènica del Llevant i almenys sis d'elles són de la tipologia anomenada coves de la zona de mescla costanera. La cavitat més destacada del treball és la cova Genovesa o cova d'en Bessó amb un recorregut projectat de 2447 m dels quals 1845 m són subaquàtics.[eng] We present the surveys and descriptions of seven costal-lying caves within the Portocristo Novo urbanisation, Manacor municipal district. These caves are located in a tabular platform postorogenetic to the Serres Llevant and at least six of them having a typology associated with the costal mixing-zone. The most noteworthy cave is the Cova Genovesa, or Cova d'en Bessó, with a survey length of 2447 m (1845 m subaquatic).[spa] Presentamos la topografía y la descripción de siete cavidades del litoral de Manacor, situadas en la urbanización de Portocristo Novo. Las formaciones endokársticas se localizan en la plataforma tabular postorogénica del Llevant y al menos seis de ellas pertenecen a la tipología denominada cuevas de la zona de mezcla costera. La cavidad más destacada del trabajo es la Cova Genovesa o Cova d'en Bessó con un recorrido proyectado de 2447 m de los cuales 1845 m. son subacuáticos